The box below forms a basis for a game between two players. The idea is that the two players take turns shading in one of the six rectangles (numbered 1 through 6) with one of two colors- say red or blue.

Either player can use either color on any turn. It is illegal to shade a rectangle with a color that has already been given to a neighboring rectangle. If you don't have a legal move at your turn, you lose the game.

Prove that for each opening move by the first player, the second player can always win.